Piezoelectric transducer (PZT) patches can be attached to a structure in order to reduce vibration. The PZT patches essentially convert vibrational mechanical energy into electrical energy. The electrical energy can be dissipated via an electrical impedance. Currently, impedance designs require experimental tuning of resistive circuit elements to provide optimal performance. A systematic method is presented for determining the resistance values by minimizing the H₂ norm of the damped system. After the design process, shunt circuits are normally implemented using discrete resistors, virtual inductors and Riordian gyrators. The difficulty in constructing the shunt circuits and achieving reasonable performance has been an ongoing and unaddressed problem in shunt damping. A new approach to implementing piezoelectric shunt circuits is presented. A synthetic impedance, consisting of a voltage controlled current source and a digital signal processor system, is used to synthesize the terminal impedance of a shunt network. A two-mode shunt circuit is designed and implemented for an experimental simply supported beam. The second and third structural modes of the beam are reduced in magnitude by 22 and 18 dB.